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Register a new userStatistics of roughness for fluctuating interfaces: A survey of different scaling analyses
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Added by
Sebastian Bustingorry
Publication date
2019
fields
Physics
and research's language is
English
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Ferroic domain walls are known to display the characteristic scaling properties of self-affine rough interfaces. Different methods have been used to extract roughness information in ferroelectric and ferromagnetic materials. Here, we review these different approaches, comparing roughness scaling analysis based on displacement autocorrelation functions in real space, both locally and globally, to reciprocal space methods. This allows us to address important practical issues such as the necessity of a sufficient statistical averaging. As an ideal, artifact-free reference case and particularly targeting finite-size systems, we consider two cases of numerically simulated interfaces, one in equilibrium with a disordered energy landscape and one corresponding to the critical depinning state when the external applied driving force equals the depinning force. We find that the use of the reciprocal space methods based on the structure factor allows the most robust extraction of the roughness exponent when enough statistics is available, while real space analysis based on the roughness function allows the most efficient exploitation of a dataset containing only a limited number of interfaces of variable length. This information is thus important for properly quantifying roughness exponents in ferroic materials.
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Self-affine rough interfaces are ubiquitous in experimental systems, and display characteristic scaling properties as a signature of the nature of disorder in their supporting medium, i.e. of the statistical features of its heterogeneities. Different methods have been used to extract roughness information from such self-affine structures, and in particular their scaling exponents and associated prefactors. Notably, for an experimental characterization of roughness features, it is of paramount importance to properly assess sample-to-sample fluctuations of roughness parameters. Here, by performing scaling analysis based on displacement correlation functions in real and reciprocal space, we compute statistical properties of the roughness parameters. As an ideal, artifact-free reference case study and particularly targeting finite-size systems, we consider three cases of numerically simulated one-dimensional interfaces: (i) elastic lines under thermal fluctuations and free of disorder, (ii) directed polymers in equilibrium with a disordered energy landscape, and (iii) elastic lines in the critical depinning state when the external applied driving force equals the depinning force set by disorder. Our results shows that sample-to-sample fluctuations are rather large when measuring the roughness exponent. These fluctuations are also relevant for roughness amplitudes. Therefore a minimum of independent interface realizations (at least a few tens in our numerical simulations) should be used to guarantee sufficient statistical averaging, an issue often overlooked in experimental reports.
Fluctuations of the interface between coexisting colloidal fluid phases have been measured with confocal microscopy. Due to a very low surface tension, the thermal motions of the interface are so slow, that a record can be made of the positions of the interface. The theory of the interfacial height fluctuations is developed. For a host of correlation functions, the experimental data are compared with the theoretical expressions. The agreement between theory and experiment is remarkably good.
Domain-wall dynamics and spatial fluctuations are closely related to each other and to universal features of disordered systems. Experimentally measured roughness exponents characterizing spatial fluctuations have been reported for magnetic thin films, with values generally different from those predicted by the equilibrium, depinning and thermal reference states. Here, we study the roughness of domain walls in GdFeCo thin films over a large range of magnetic field and temperature. Our analysis is performed in the framework of a model considering length-scale crossovers between the reference states, which is shown to bridge the differences between experimental results and theoretical predictions. We also quantify for the first time the size of the depinning avalanches below the depinning field at finite temperatures.
The creep motion of domain walls driven by external fields in magnetic thin films is described by universal features related to the underlying depinning transition. One key parameter in this description is the roughness exponent characterizing the growth of fluctuations of the domain wall position with its longitudinal length scale. The roughness amplitude, which gives information about the scale of fluctuations, however, has received less attention. Albeit their relevance, experimental reports of the roughness parameters, both exponent and amplitude, are scarce. We report here experimental values of the roughness parameters for different magnetic field intensities in the creep regime at room temperature for a Pt/Co/Pt thin film. The mean value of the roughness exponent is $zeta = 0.74$, and we show that it can be rationalized as an effective value in terms of the known universal values corresponding to the depinning and thermal cases. In addition, it is shown that the roughness amplitude presents a significant increase with decreasing field. These results contribute to the description of domain wall motion in disordered thin magnetic systems.
A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers of mass remain separated by a nonzero distance $ell$. Here we examine the statistics of $ell$ at the time of first contact for surfaces that evolve in time according to the Edwards-Wilkinson equation. We present a general approach to calculate its probability distribution and determine how its most likely value $ell^*$ depends on the surfaces lateral size $L$. We are motivated by an interest in the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Computer simulations of this scenario verify the predicted scaling behavior in two and three dimensions. In the latter case, slow growth where $ell^ast$ is an algebraic function of $log L$ implies that slab-shaped domains remain topologically intact until $ell$ becomes very small, contradicting expectations from equilibrium thermodynamics.
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